can someone help me in this problem??

[sungjin6458]

"A club has 15 members consisting of seniors and juniors. After seven more seniors and three more juniors join the club, the ratio of juniors is 2 to 3. How many juniors are now in the club?" the answer is 7, it says, but doesnt say how! thank you in advance.

 

[tkhunny]

"A club has 15 members consisting of seniors and juniors. After seven more seniors and three more juniors join the club, the ratio of juniors is 2 to 3. How many juniors are now in the club?"

Name Stuff.
Name What?
What does it want?
"How many juniors are now in the club?"
Name that.

I'm not quite sure what "now" means. I'll use ORIGINAL.
x = Number of Juniors originally in the club.

Thus,

15 - x = Number of Seniors in the club.

"seven more seniors and three more juniors join the club"

15 - x + 7 = New Number of Seniors = 22 - x
x + 3 = New Number of Juniors

"ratio of juniors [to seniors?] is 2 to 3"

(x+3)/(22 - x) = 2/3

Solve for 'x'

In case I guessed wrong:

"ratio of [seniors to?] juniors is 2 to 3"

(22 - x)/(x+3) = 2/3

Unfortunately, both lead to a positive integer solution, so you'll have to decide which way to go.

In case I guessed wrong again, x+3 would be the right answer.

With:
"ratio of juniors [to seniors?] is 2 to 3" and
"now" means Originally,
I get x = 7.

The world needs better transcription of better problem statements.

 

[soroban]

Hello, sungjin6458!

If you can handle <u>two</u> variables, here's another approach.

A club has 15 members consisting of seniors and juniors.
After seven more seniors and three more juniors join the club, the ratio of juniors is 2 to 3.
How many juniors are now in the club?

The answer is 7, it says, but doesnt say how! . . . Of course not!

Let J = number of juniors (now).
Let S = number seniors (now).

We already know that: . J + S .= .15 . [1]

Three more juniors join: . J + 3
Seven more seniors join: . S + 7

. . . . . . . . . . . . . . . . .J + 3 . . . . .2
This ratio is 2 to 3: . ------- . = . ---
. . . . . . . . . . . . . . . . .S + 7 . . . . 3

. . . which simplifies to: . 3J - 2S .= .5 . [2]


Then solve the system of equations: .[1] and [2].

[By the way, this does NOT belong in the Calculus section . . . you know that!]